Probably from Middle English bibbento drink heartilyfrom Latin biberepō(i)- in Indo-European roots
American Heritage Dictionary of the English Language, 5th Edition
Originally verb sense “drink heartily”, from Middle English bibben, either from Latinbibō (“I drink”), from Proto-Indo-European*peh₃-, or of imitative origin. Noun sense (clothing) presumably either because worn while drinking, or because the clothing itself “drinks up” spills.
Bib Sentence Examples
An elderly man in bib overhauls alighted and went in the building.
In 1868 the reigning chief, Bib Doda, died, and his son and successor Prenk was detained as a hostage by the Turks.
For example, one set might have a small beanie cap, onesie, leggings and bib.